{"id":{"repo_id":"iupui","oai_identifier":"oai:scholarworks.indianapolis.iu.edu:1805/22680"},"canonical_url":"https://search.dev.ndltd.org/etd/iupui/oai:scholarworks.indianapolis.iu.edu:1805/22680","repository":{"repo_id":"iupui","name":"IUPUI","base_url":"https://scholarworks.indianapolis.iu.edu/server/oai/request"},"display":{"title":"Ricci Curvature of Finsler Metrics by Warped Product","abstract":"In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.","abstract_html":"In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes.","abstract_has_math":false,"creators":["Marcal, Patricia"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Shen, Zhongmin"],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-05","date_published":"2020-05","updated_at":"2026-07-24T02:41:30Z","subjects":["Warped Product","Finsler Metrics","Ricci Curvature","Ricci flat"],"languages":["en_US"],"rights":["Attribution-NonCommercial-ShareAlike 4.0 International"],"rights_urls":["http://creativecommons.org/licenses/by-nc-sa/4.0/"],"identifier_entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://dx.doi.org/10.7912/C2/2410"],"render_values":[{"text":"http://dx.doi.org/10.7912/C2/2410","href":"http://dx.doi.org/10.7912/C2/2410","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/1805/22680","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Shen, Zhongmin"]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Buse, Olguta","Ramras, Daniel","Roeder, Roland"]},{"key":"dc:creator","label":"Author","values":["Marcal, Patricia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-05-01T18:15:29Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-05-01T18:15:29Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-05"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Warped Product","Finsler Metrics","Ricci Curvature","Ricci flat"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Attribution-NonCommercial-ShareAlike 4.0 International"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by-nc-sa/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1805/22680","http://dx.doi.org/10.7912/C2/2410"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Indiana University-Purdue University Indianapolis (IUPUI)"]},{"key":"dc:description.abstract","label":"Abstract","values":["In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes."]},{"key":"dc:title","label":"Title","values":["Ricci Curvature of Finsler Metrics by Warped Product"]}]}],"canonical_facts":{"dc:contributor.advisor":["Shen, Zhongmin"],"dc:contributor.other":["Buse, Olguta","Ramras, Daniel","Roeder, Roland"],"dc:creator":["Marcal, Patricia"],"dc:date.accessioned":["2020-05-01T18:15:29Z"],"dc:date.available":["2020-05-01T18:15:29Z"],"dc:date.issued":["2020-05"],"dc:description":["Indiana University-Purdue University Indianapolis (IUPUI)"],"dc:description.abstract":["In the present work, we consider a class of Finsler metrics using the warped product notion introduced by B. Chen, Z. Shen and L. Zhao (2018), with another “warping”, one that is consistent with the form of metrics modeling static spacetimes and simplified by spherical symmetry over spatial coordinates, which emerged from the Schwarzschild metric in isotropic coordinates. We will give the PDE characterization for the proposed metrics to be Ricci-flat and construct explicit examples. Whenever possible, we describe both positive-definite solutions and solutions with Lorentz signature. For the latter, the 4-dimensional metrics may also be studied as Finsler spacetimes."],"dc:identifier.uri":["https://hdl.handle.net/1805/22680","http://dx.doi.org/10.7912/C2/2410"],"dc:language.iso":["en_US"],"dc:rights":["Attribution-NonCommercial-ShareAlike 4.0 International"],"dc:rights.uri":["http://creativecommons.org/licenses/by-nc-sa/4.0/"],"dc:subject":["Warped Product","Finsler Metrics","Ricci Curvature","Ricci flat"],"dc:title":["Ricci Curvature of Finsler Metrics by Warped Product"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T02:41:30Z"}